Question

What is the equivalent resistance of two resistance of 10 home's that are connected in parallel with each other

Answer 1

Appropriate Question :-

• What is the equívalent resístance of two resístance of 10 ohm that are cónnected in párallel with each other.

Given :-

• The two resístance of 10 ohm that are connected in párallel with each other.

To Find :-

• What is the equívalent resístance.

Formula Used :-

$\clubsuit$Equívalent Resístance for párallel connection :

$\begin{gathered}\mapsto \sf\boxed{\bold{\pink{\dfrac{1}{R_{eq}} =\: \dfrac{1}{R_1} + \dfrac{1}{R_2} + . . . . \dfrac{1}{R_n}}}}\\\end{gathered}$

where,

• Resístance of resístors R₁ = 10 ohm
• Resístance of resístors R₂ = 10 ohm

According to the question by using the formula we get,

$\longrightarrow \sf \dfrac{1}{R_{eq}} =\: \dfrac{1}{10} + \dfrac{1}{10}$

$\longrightarrow \sf \dfrac{1}{R_{eq}} =\: \dfrac{1 + 1}{10}$

$\longrightarrow \sf \dfrac{1}{R_{eq}} =\: \dfrac{2}{10}$

$\longrightarrow \sf 2 \times R_{eq} =\: 10 \times 1$

$\longrightarrow \sf 2R_{eq} =\: 10$

$\longrightarrow \sf R_{eq} =\: \dfrac{\cancel{10}}{\cancel{2}}$

$\longrightarrow \sf R_{eq} =\: \dfrac{5}{1}$

$\longrightarrow \sf\bold{\red{R_{eq} =\: 5\: \text{\O}mega}}$

∴ The equívalent resístance is 5 Ω .

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EXTRA INFORMATION :-

$\clubsuit$ Equívalent Resístance for series connection :

$\begin{gathered}\mapsto \sf\boxed{\bold{\pink{R_{eq} =\: R_1 + R_2\: . . . .\: R_n}}}\\\end{gathered}$

where,

Req =equivalent resistors

R₁ = Resístance of resístors R₁

R₂ = Resístance of resístors R₂